You rush a miraclemaker and you get lousy miracles.

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You rush a miracle-maker and you get lousy
miracles.
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• Billy Crystal in The Princess Bride (1987)

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Computer Science 101Lecture 8
www.pjrc.com/tech/ 8051/board5/schematic.gif

• Spring Semester 2008
• Monday, January 28
• Week 4/18
• Albert H. Carlson

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Announcements

• HW 2 is due on Friday, February 8

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Division

• Said to be confusing, but after practice, it is
  not
• A lot like normal decimal division
• Remember, you can only use 1 and 0. Either it
  goes in, or it does not. It is that simple
• Set it up just like you normally do for decimal
  division

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An Example
0110/0010
Lets forget the leading 0s on 0010
0
0
1
1
10 / 0110
10
1
0
10
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Practice Problems
1010/0011
11r1
1101/0010
110r1
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Convert Between Bases

• Sometimes it is important to be able to convert a
  number in one base to another
• We are primarily concerned with decimal to
  binary, and back
• Sometimes we need to convert from strange bases
  to other bases
• Fortunately, the procedure is easy and very
  regular

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• We are going back to what we did on binary
• Here we make columns based on powers of the base
• Usually, it is easiest to convert to base 10 and
  then convert to the target base

b0
b1
b2
b3

bn
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• What we do is to calculate the value of the
  number in base 10. We have done this before
• Next, we create the columns in the target base
• Then we figure out how much goes in each of the
  new columns in the target base

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An Example
21123 to base 7
27 9 3 1
68

• Convert to base 10

2 1 1 2
- 0 68
1a. Make the base column list
2. Calculate the Sum
1
7
49
343
-49 19
2 1 2
3. Make the target base column list
0
1
2
5
1 3 3
1 9 9
-14 5
2 27 54
21123 01257
68
-5 0
Stop when the column is MORE than the number
4. Start subtracting from highest number
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Practice Problems
1000002 to Hex
20H
72158 to decimal
3725
73209 to base 5
124305
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MSB and LSB

• When we write a number, we need to know what
  order it is written in
• By convention we make the smallest number column
  on the right
• Because this column has the lowest weight, it is
  called the Least Significant Bit, or LSB
• The column on the left is the Most Significant
  Bit, or MSB

M L S S B B 1000000
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Big vs Little Endian

• Big Endian
• L M
• S S
• B B
• Little Endian
• M L
• S S
• B B

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Statistics

• A common use of the computer is to take and
  analyze statistics
• Statistics are used to find underlying
  information about data
• It starts by asking a question that can be
  characterized by data
• Then you go off and collect data about the
  question and record it

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The Solution Space

• Lets say we want to measure something about an
  experiment
• We will define an experiment as a repeatable
  test, like flipping a coin
• All of the possible outcomes of the experiment
  can be listed in a space, called the solution
  space

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Solution Space

• For example, the solution space for flipping a
  coin is
• Head,Tail
• For rolling a dice the solution space is
• 1,2,3,4,5,6
• For one of my exams, the solution space is
• 0,100

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Questions?